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Shape optimization in contact problems based on penalization of the state inequality

Jaroslav Haslinger, Pekka Neittaanmäki, Timo Tiihonen (1986)

Aplikace matematiky

The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.

Shape optimization of an elasto-perfectly plastic body

Ivan Hlaváček (1987)

Aplikace matematiky

Within the range of Prandtl-Reuss model of elasto-plasticity the following optimal design problem is solved. Given body forces and surface tractions, a part of the boundary, where the (two-dimensional) body is fixed, is to be found, so as to minimize an integral of the squared yield function. The state problem is formulated in terms of stresses by means of a time-dependent variational inequality. For approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant...

Shape optimization of an elasto-plastic body for the model with strain- hardening

Vladislav Pištora (1990)

Aplikace matematiky

The state problem of elasto-plasticity (for the model with strain-hardening) is formulated in terms of stresses and hardening parameters by means of a time-dependent variational inequality. The optimal design problem is to find the shape of a part of the boundary such that a given cost functional is minimized. For the approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular elements for the stress and the hardening parameter, and backward differences...

Shape optimization of elastoplastic bodies obeying Hencky's law

Ivan Hlaváček (1986)

Aplikace matematiky

A minimization of a cost functional with respect to a part of the boundary, where the body is fixed, is considered. The criterion is defined by an integral of a yield function. The principle of Haar-Kármán and piecewise constant stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.

Singular Perturbations For Heart Image Segmentation Tracking

J. Pousin (2009)

Mathematical Modelling of Natural Phenomena

In this note we give a result of convergence when time goes to infinity for a quasi static linear elastic model, the elastic tensor of which vanishes at infinity. This method is applied to segmentation of medical images, and improves the 'elastic deformable template' model introduced previously.

Slab analogy in theory and practice of conforming equilibrium stress models for finite element analysis of plane elastostatics

Miroslav Vondrák (1985)

Aplikace matematiky

The fundamental problem in the application of the principle of complementary energy is the construction of suitable subsets that approximate the set of all statically admissible fields satisfying both the conditions of equilibrium inside the body and the static boundary conditions. The notion “slab analogy” is motivated and the interface conditions for the Airy stress function are established at the contact of two domains. Some spaces of types of conforming equilibrium stress elements, which can...

Some new technics regarding the parallelisation of ZéBuLoN, an object oriented finite element code for structural mechanics

Frédéric Feyel (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A finite element code, called ZéBuLoN was parallelised some years ago. This code is entirely written using an object oriented framework (C++ is the support language). The aim of this paper is to present some problems which arose during the parallelization, and some innovative solutions. Especially, a new concept of message passing is presented which allows to take into account SMP machines while still using the parallel virtual machine abstraction.

Some new technics regarding the parallelisation of ZéBuLoN, an object oriented finite element code for structural mechanics

Frédéric Feyel (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

A finite element code, called ZéBuLoN was parallelised some years ago. This code is entirely written using an object oriented framework (C++ is the support language). The aim of this paper is to present some problems which arose during the parallelization, and some innovative solutions. Especially, a new concept of message passing is presented which allows to take into account SMP machines while still using the parallel virtual machine abstraction.

Special exact curved finite elements

Jitka Křížková (1991)

Applications of Mathematics

Special exact curved finite elements useful for solving contact problems of the second order in domains boundaries of which consist of a finite number of circular ares and a finite number of line segments are introduced and the interpolation estimates are proved.

Stability of finite element mixed interpolations for contact problems

Klaus Jürgen Bathe, Franco Brezzi (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We consider the formulation of contact problems using a Lagrange multiplier to enforce the contact no-penetration constraint. The finite element discretization of the formulation must satisfy stability conditions which include an inf-sup condition. To identify which finite element interpolations in the contact constraint lead to stable (and optimal) numerical solutions we focus on the finite element discretization and solution of a «simple» model problem. While a simple problem to avoid the need...

Stability of microstructure for tetragonal to monoclinic martensitic transformations

Pavel Belik, Mitchell Luskin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We give an analysis of the stability and uniqueness of the simply laminated microstructure for all three tetragonal to monoclinic martensitic transformations. The energy density for tetragonal to monoclinic transformations has four rotationally invariant wells since the transformation has four variants. One of these tetragonal to monoclinic martensitic transformations corresponds to the shearing of the rectangular side, one corresponds to the shearing of the square base, and one corresponds to...

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